Q. For a fist order reaction, the concentration changes from 0.8 to 0.4 in 15 min. The time taken for the concentration to change from 0.1 M to 0.025 M is
A) 30 Min
B) 15 Min
C) 7.5 min
D) 60 min
Explanation
(a)
$T_{50} = 15\ min$
$k = \frac{2.303log2}{T_{50}} = \frac{2.303log2}{15}$
a=0.1M
$(a - x) = 0.025\ M$
For first order reaction,
$k = \frac{2.303log2}{T_{50}}\log\left( \frac{a}{a - x} \right)$
$\frac{2.303log2}{15} = \frac{2 \times 2.303log2}{t}\log\frac{0.1}{0.025}$
$= \frac{2.303}{t}log4$
$\therefore\frac{2.303log2}{15} = \frac{2 \times 2.303log2}{t}$
$\therefore$ t=30 min
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.